pH titration has traditionally been one of the simplest and commonly used methods of chemical analysis. Present pH titration practice is to use automatic potentiometric titrators whenever possible because of their cost effectiveness and assistance in laboratory record keeping. Such instruments deliver a titrant at a programmed (i.e., constant or variable) rate. They measure and record the sample solution pH at short time intervals to generate tens to hundreds of data points, and calculate from the recorded data one or more titration equivalence points (henceforth "end points") from their sample concentration(s). They typically make titration less labor intensive than known manual methods and yield more objective and usually more accurate results. However, automatic potentiometric titrators typically do not make full use of the abundant data they can collect. Instead, only a few data points near a titration end point are used for calculations.
As a result, the well known problems with pH titration that have limited its usefulness still persist. For example, unless two acid or base components have acidity constants ("Ka's") that differ by about four (4) orders of magnitudes (i.e., 4 logarithmic "pK.sub.a " units or more), their individual concentrations generally cannot be accurately determined by one titration. Instead, only a "total titratable acid/base" result is determinable. Also, it is difficult to analyze very weak acids or bases using known methods because the titration end point, occurring at a pH close to the pH of the titrant, is poorly defined. Similarly, the combination of medium strength acids (i.e., pK.sub.a .congruent.2-3.5) and strong acids cannot be accurately analyzed when in the presence of one another. The same result occurs when analyzing medium strength bases (i.e., pK.sub.a .congruent.10.5-12) and strong bases.
Another difficulty with known titration methods is that, to define a titration end point, a sample sometimes has to be titrated to pH values that are either acidic or basic enough to cause the degradation or precipitation of acid or base-sensitive species. Weak acid or base titrants often cannot be used because the resulting end points, which are needed when using prior art methods, will be poorly defined. Finally, even if a chemical analysis can be performed, the customary graphical representations of pH titration do not typically convey explicit information about the identity of the titrated species.
The inventors are aware of a method of calculating the titration end point, called the Gran technique, which uses more data points. Used commercially in a titration system made by Orion, the method attempts to accurately define a titration end point by an extrapolation algorithm, and can be useful in the titration of very weak acids or bases. Another titration system, made by Sanda Corporation, utilizes the experimental method of thermometric titration in an effort to determine individual concentrations when two acids or bases have dissociation constants that differ by at least 2 pK.sub.a units. Yet, even these two titration methods still focus on a titration end point, are unable to resolve the situation of closely spaced pK.sub.a 's, and yield little information about the pK.sub.a 's, and therefore the identities, of components in mixtures.